(CBS News) Engaging in a good-natured battle of wiles, President Obama and Vice President Joe Biden last month welcomed to 1600 Pennsylvania Avenue 108-year-old Lucy Coffey, the oldest living female veteran in the United States.

A video released Tuesday by the White House shows a seemingly impromptu appearance by the president while Coffey was meeting with Biden during her two-day visit to the nation's capital in July. Handing Coffey - a veteran of the Women's Army Corps in World War II - a presidential command coin, Mr. Obama assured that he only doles those out to his "good friends," adding, "we're so proud of you and proud of your service."

Lucy Coffey is the oldest living female veteran. At 108 years old, she's still making new friends. She recently had a visit with Vice President Joe Biden, and even President Obama stopped by to say hello.

Turning on the charm, Biden told Coffey she's "a special lady." And not to be outdone, he offered up his own command coin, but qualified that he recognizes it wasn't as "prestigious" as the president's gift "because it has that word 'vice' in front of it."

Mr. Obama's brief visit, the vice president said, "reminds me of every time I had a good-looking date - there'd be some better-looking guy coming along. You know what I mean? I'm vice president; the president comes in, and everybody drops everything. You know what I mean?

"...But I'm the guy that loves ya," he added, eliciting laughter from Coffey.

Biden wrapped up by showing off an election-day photo of his mother, who recently passed away, as well as one of his German Shepard, Champ. As party favors, he handed out stuffed versions of "the best dog in the world" to Coffey and her company.

In spite of Biden's best efforts, though, it's likely Coffey's favorite takeaway was the photograph she posed for with Mr. Obama - or the kiss on the cheek he left her. As one of her guests told the president: "She has your picture in her bedroom."